cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-3 of 3 results.

A175314 Decimal expansion of exp(Pi) + exp(-Pi).

Original entry on oeis.org

2, 3, 1, 8, 3, 9, 0, 6, 5, 5, 1, 0, 4, 3, 0, 4, 1, 2, 5, 5, 5, 0, 3, 5, 0, 4, 1, 0, 5, 1, 2, 0, 2, 7, 5, 3, 9, 1, 5, 4, 1, 8, 3, 4, 3, 5, 2, 4, 1, 0, 8, 4, 5, 0, 7, 6, 4, 2, 5, 7, 6, 6, 0, 9, 6, 9, 2, 5, 3, 9, 3, 1, 1, 6, 4, 4, 7, 4, 7, 0, 7, 5, 1, 2, 1, 5, 1, 1, 1, 9, 5, 7, 0, 2, 9, 4, 5, 0, 3, 0, 4, 0, 6, 2, 9
Offset: 2

Views

Author

R. J. Mathar, Apr 01 2010

Keywords

Examples

			23.1839065510430412555035041051202753...

Links

Crossrefs

Cf. A039661 (exp(Pi)), A093580 (exp(-Pi)), A175315, A334402 (cosh(Pi)).

Programs

Formula

Equals A039661 + A093580.
Equals 2*cosh(Pi).
Equals 10 * Product_{k>=1} (1 + 4/(2*k+1)^2). - Amiram Eldar, Aug 09 2020

A334401 Decimal expansion of sinh(Pi).

Original entry on oeis.org

1, 1, 5, 4, 8, 7, 3, 9, 3, 5, 7, 2, 5, 7, 7, 4, 8, 3, 7, 7, 9, 7, 7, 3, 3, 4, 3, 1, 5, 3, 8, 8, 4, 0, 9, 6, 8, 4, 4, 9, 5, 1, 8, 9, 0, 6, 6, 3, 9, 4, 7, 8, 9, 4, 5, 5, 2, 3, 2, 1, 6, 3, 3, 6, 1, 0, 6, 1, 6, 4, 5, 7, 9, 2, 4, 6, 6, 7, 1, 7, 4, 0, 7, 9, 0, 9, 4, 1, 6, 0, 1, 8, 5, 5, 2, 8, 2, 4, 0, 6, 7, 6, 4, 4, 4, 6, 7, 9, 4, 8
Offset: 2

Views

Author

Ilya Gutkovskiy, Apr 26 2020

Keywords

Comments

This constant is transcendental.

Examples

			(e^Pi - e^(-Pi))/2 = 11.5487393572577483779773343153884...

Links

Crossrefs

Cf. A000796, A001113, A039661, A068470, A073742, A093580, A156648, A323983, A334402.

Programs

  • Mathematica
    RealDigits[Sinh[Pi], 10, 110] [[1]]

Formula

Equals Sum_{k>=0} Pi^(2*k+1)/(2*k+1)!.
Equals 2 * Product_{k>=1} (4*k^2+4)/(4*k^2-1).

A330865 Decimal expansion of cosh(Pi/2)/Pi.

Original entry on oeis.org

7, 9, 8, 6, 9, 6, 3, 1, 5, 9, 5, 6, 4, 6, 3, 0, 8, 4, 8, 6, 3, 8, 0, 6, 7, 0, 4, 2, 2, 1, 0, 9, 6, 1, 3, 8, 6, 9, 1, 4, 9, 2, 8, 7, 4, 1, 8, 5, 1, 2, 9, 1, 2, 3, 4, 8, 3, 7, 2, 6, 6, 4, 0, 6, 4, 5, 9, 0, 2, 4, 3, 1, 1, 2, 9, 6, 8, 6, 5, 4, 3, 0, 6, 7, 6, 6, 4, 1, 0, 6, 5, 9, 8, 7, 3, 9, 6, 2, 3, 2, 2, 2, 5, 7, 1, 0, 1, 5, 8, 5
Offset: 0

Views

Author

Ilya Gutkovskiy, Apr 28 2020

Keywords

Examples

			(1 - 1/2^2) * (1 + 1/3^2) * (1 - 1/4^2) * (1 + 1/5^2) * (1 - 1/6^2) * ... = (e^(Pi/2) + e^(-Pi/2))/(2*Pi) = 0.7986963159564630848638067...

Crossrefs

Cf. A042972, A049006, A049541, A156648, A175615, A308715, A308716, A308718, A323982, A330864, A334402.

Programs

  • Mathematica
    RealDigits[Cosh[Pi/2]/Pi, 10, 110] [[1]]
  • PARI
    cosh(Pi/2)/Pi \\ Michel Marcus, Apr 28 2020

Formula

Equals Sum_{k>=0} Pi^(2*k-1)/(4^k*(2*k)!).
Equals Product_{k>=2} (1 - (-1)^k/k^2).
Equals (i^(-i) + i^i)/(2*Pi), where i is the imaginary unit.
Showing 1-3 of 3 results.

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